The newly developed proton-electrostatics localization hypothesis in understanding proton-coupling bioenergetics over the Nobel-prize work of Peter Mitchell's chemiosmotic theory (Lee 2012 Bioenergetics 1:104; doi:10.4172/2167-7662.1000104) resulted in the following new proton motive force (pmf) equation that may potentially represent a major breakthrough advance in the science of bioenergetics:
                              pmf          ⁡                      (                          Δ              ⁢                                                          ⁢              p                        )                          =                              Δ            ⁢                                                  ⁢            ψ                    +                                                    2.3                ⁢                RT                            F                        ⁢                          (                                                pH                  nB                                +                                                      log                    10                                    (                                                                                    c                        s                                            ·                                              Δψ                                                  l                          ·                                                      F                            ⁡                                                          (                                                                                                ∏                                                                      i                                    =                                    1                                                                    n                                                                ⁢                                                                                                                                  ⁢                                                                  {                                                                                                                                                    K                                        Pi                                                                            ⁡                                                                              (                                                                                                                              [                                                                                          M                                              pB                                                                                              i                                                +                                                                                                                                      ]                                                                                                                                [                                                                                          H                                              pB                                              +                                                                                        ]                                                                                                                          )                                                                                                              +                                    1                                                                    }                                                                                            )                                                                                                                                            +                                          [                                              H                        pB                        +                                            ]                                                        )                                            )                                                          [        1        ]            Where Δψ is the electrical potential difference across the membrane; pHnB is pH of the cytoplasmic bulk phase; [H+pB] is the proton concentration in the periplasmic bulk aqueous phase; C/S is the specific membrane capacitance; l is the thickness for localized proton layer; KPi is the equilibrium constant for non-proton cations (Mi+pB) to exchange for localized protons; and [Mi+pB] is the concentration of non-proton cations in liquid culture medium (Lee 2015 Bioenergetics 4: 121. doi:10.4172/2167-7662.1000121).
The core concept of the proton-electrostatics localization hypothesis is based on the premise that a biologically-relevant water body, such as the water within a bacterium, can act as a proton conductor in a manner similar to an electric conductor with respect to electrostatics. This is consistent with the well-established knowledge that protons can quickly transfer among water molecules by the “hops and turns” mechanism. From the charge translocation point of view, it is noticed that hydroxyl anions are transferred in the opposite direction of proton conduction. This understanding suggests that excess free protons in a biologically-relevant water body behave like electrons in a perfect conductor. It is well known for a charged electrical conductor at static equilibrium that all extra electrons reside on the conducting body's surface. This is expected because electrons repel each other, and, being free to move, they will spread out to the surface. By the same token, it is reasonable to expect that free excess protons (or conversely the excess hydroxyl anions) in a biologically-relevant water body will move to its surface. Adapting this view to excess free hydroxyl anions in the cytoplasm (created by pumping protons across the cytoplasm membrane through the proton-transfer-coupled respiratory electron transport into the liquid medium outside the cell), they will be electrostatically localized along the water-membrane interface at the cytoplasmic (n) side of the cell membrane. In addition, their negative charges (OH−) will attract the positively charged species (H+) outside the cell to the membrane-water interface at the periplasmic (p) side.
That is, when excess hydroxyl anions are created in the cytoplasm by the oxidative-driven proton pump across the membrane leaving excess protons outside the cell, the excess hydroxyl anions in the cytoplasm will not stay in the bulk water phase because of their mutual repulsion. Consequently, they go to the water-membrane interface at the cytoplasmic side of the membrane where they then attract the excess protons at the periplasmic side of the membrane, forming an “excess anions-membrane-excess protons” capacitor-like system. Therefore, the proton capacitor concept is used to calculate the effective concentration of the localized protons [HL+]0 at the membrane-water interface in a pure water-membrane-water system assuming a reasonable thickness (l) for the localized proton layer using the following equation:
                                          [                          H              L              +                        ]                    0                =                                            C              S                        ·                          Δψ                              l                ·                F                                              =                                    Δψ              ·              κ              ·                              ɛ                0                                                    d              ·              l              ·              F                                                          [        2        ]            where C/S is the membrane capacitance per unit surface area; F is the Faraday constant; κ is the dielectric constant of the membrane; εo is the electric permittivity; d is the thickness of the membrane; and l is the thickness of the localized proton layer. This proton-capacitor equation [2] is a foundation for the newly revised pmf equation [1], which includes an additional term that accounts for the effect of non-proton cations exchanging with the localized protons.
Recently, using nanoscale measurements with electrostatic force microscopy, the dielectric constant (κ) of a lipid bilayer was determined to be about 3 units, which is in the expected range of 2˜4 units (Grames et al, Biophysical Journal 104: 1257-1262; Heimburg 2012 Biophysical Journal 103: 918-929.). Table 1 lists the calculation results for localized protons for a theoretical pure water-membrane-water system with Eq. 2 using a lipid membrane dielectric constant κ of 3 units, membrane thickness d of 4 nm, trans-membrane potential difference Δψ of 180 mV, and three assumed values for the proton layer thickness of 0.5, 1.0, and 1.5 nm.
TABLE 1Calculation of localized protons with Equation 2 in a theoreticalpure water-membrane-water system using a membranedielectric constant κ of 3, membranethickness d of 4 nm, and trans-membrane potentialdifference Δψ of 180 mV.Assumed thickness (l) of 0.5 nm 1.0 nm 1.5 nmlocalized proton layerLocalized proton density per1.238 × 10−81.238 × 10−81.238 × 10−8unit area (moles H+/m2)Effective concentration of24.76 mM12.38 mM8.25 mMlocalized proton ([HL+]0)Effective pH of localized1.611.912.08proton layer (pHL0)
As shown in Table 1, the localized proton density per unit area was calculated to be 1.238×10−8 moles H+/m2. The calculated effective concentration of localized proton ([HL+]0) was in a range from 8.25 mM to 24.76 mM if the localized proton layer is around 1.0±0.5 nm thick. The calculated effective pH of localized proton layer (pHL0) was 1.61, 1.91, and 2.08 assuming that the localized proton layer is 0.5, 1.0, and 1.5-nm thick, respectively. This calculation result also indicated that localized excess protons may be created at a water-membrane interface for possible industrial applications such as acid-etching of certain metals and/or protonation of certain micro/nanometer materials without requiring the use of conventional acid chemicals such as nitric and sulfuric acids.